Research Activities
My research statement is available upon request.
Research Interests
My research interests are in low-dimensional topology and geometric group theory. These two closely related areas have always enriched each other. I primarily focus on questions regarding 3-manifolds and their Heegaard splittings, knot theory, hyperbolic geometry, hyperbolic and relatively hyperbolic groups, mapping class groups, and the interplay between them.
Research Articles
Once ready for publication, all of my articles will be posted on arXiv. The expanded list, containing a brief description for each of my article, can be found here.
The Girth-Alternative for Some Finitely Generated Groups
in preparation (being reformatted from a section of my thesis)
Fox Reimbedding and Bing Submanifolds,
preprint, October 2007 (updated on 6 Jan. 2008)
PDF PS.GZ Abstract
Research Presentations
Some of my past research presentations are listed below. The full list of my talks, including survey talks I have given at UC Davis as a graduate student, can be found on here.
AMS Mathematical Research Communities, June 2008
Snowbird, UT
Georgia Topology Conference, May 2008
University of Georgia, Athens, GA
The 11th Chico Topology Conference, May 2008
California State University, Chico, CA
International Conference on Topology and Its Applications, December 2007
Kyoto University, Kyoto, Japan
UC Davis Topology/Geometry Seminar, October 2007
University of California, Davis, CA
Lehigh University Geometry and Topology Conference, October 2007
Lehigh University, Bethelehem, PAThe 24th Annual Workshop in Geometric Topology, June 2007
Calvin College, Grand Rapids, MIThe 7th AMS-SMM Joint Meeting, May 2007
Zacatecas, Mexico
Travels
Tentative and definite future travel plans are listed below. The asterisk (*) indicates that my research will be presented. The list of my past travels can be found here.
- No upcoming travel plans at this point.
Seminars and Research Focus Groups
For the academic year 2008-2009, I am a regular participant in the Topology seminar at Oklahoma State University, Stillwater. The list of seminars and Research Focus Groups that I participated regularly in the past can be found here.Research Related Links
- Low-Dimensional Topology (Conferences, People) by M. Brittenham
- Geometric Group Theory (Conferences, People) by J. McCammond
- Computop.org by N. Dunfield
- GroupTheory.org by New York Group Theory Cooperative
- The Knot Atlas by D. Bar-Natan
- Table of Knot Invariants by C. Livingston and J. Cha
- Foliations.org by S. Hurder
